702 research outputs found
Fast Hierarchical Clustering and Other Applications of Dynamic Closest Pairs
We develop data structures for dynamic closest pair problems with arbitrary
distance functions, that do not necessarily come from any geometric structure
on the objects. Based on a technique previously used by the author for
Euclidean closest pairs, we show how to insert and delete objects from an
n-object set, maintaining the closest pair, in O(n log^2 n) time per update and
O(n) space. With quadratic space, we can instead use a quadtree-like structure
to achieve an optimal time bound, O(n) per update. We apply these data
structures to hierarchical clustering, greedy matching, and TSP heuristics, and
discuss other potential applications in machine learning, Groebner bases, and
local improvement algorithms for partition and placement problems. Experiments
show our new methods to be faster in practice than previously used heuristics.Comment: 20 pages, 9 figures. A preliminary version of this paper appeared at
the 9th ACM-SIAM Symp. on Discrete Algorithms, San Francisco, 1998, pp.
619-628. For source code and experimental results, see
http://www.ics.uci.edu/~eppstein/projects/pairs
Speeding up Cylindrical Algebraic Decomposition by Gr\"obner Bases
Gr\"obner Bases and Cylindrical Algebraic Decomposition are generally thought
of as two, rather different, methods of looking at systems of equations and, in
the case of Cylindrical Algebraic Decomposition, inequalities. However, even
for a mixed system of equalities and inequalities, it is possible to apply
Gr\"obner bases to the (conjoined) equalities before invoking CAD. We see that
this is, quite often but not always, a beneficial preconditioning of the CAD
problem.
It is also possible to precondition the (conjoined) inequalities with respect
to the equalities, and this can also be useful in many cases.Comment: To appear in Proc. CICM 2012, LNCS 736
Solving the 100 Swiss Francs Problem
Sturmfels offered 100 Swiss Francs in 2005 to a conjecture, which deals with
a special case of the maximum likelihood estimation for a latent class model.
This paper confirms the conjecture positively
An Algorithm to Construct Groebner Bases for Solving Integration by Parts Relations
This paper is a detailed description of an algorithm based on a generalized
Buchberger algorithm for constructing Groebner-type bases associated with
polynomials of shift operators. The algorithm is used for calculating Feynman
integrals and has proven itself efficient in several complicated cases.Comment: LaTeX, 9 page
Hipster: Integrating Theory Exploration in a Proof Assistant
This paper describes Hipster, a system integrating theory exploration with
the proof assistant Isabelle/HOL. Theory exploration is a technique for
automatically discovering new interesting lemmas in a given theory development.
Hipster can be used in two main modes. The first is exploratory mode, used for
automatically generating basic lemmas about a given set of datatypes and
functions in a new theory development. The second is proof mode, used in a
particular proof attempt, trying to discover the missing lemmas which would
allow the current goal to be proved. Hipster's proof mode complements and
boosts existing proof automation techniques that rely on automatically
selecting existing lemmas, by inventing new lemmas that need induction to be
proved. We show example uses of both modes
Proof-Pattern Recognition and Lemma Discovery in ACL2
We present a novel technique for combining statistical machine learning for
proof-pattern recognition with symbolic methods for lemma discovery. The
resulting tool, ACL2(ml), gathers proof statistics and uses statistical
pattern-recognition to pre-processes data from libraries, and then suggests
auxiliary lemmas in new proofs by analogy with already seen examples. This
paper presents the implementation of ACL2(ml) alongside theoretical
descriptions of the proof-pattern recognition and lemma discovery methods
involved in it
Constructing Mutually Unbiased Bases in Dimension Six
The density matrix of a qudit may be reconstructed with optimal efficiency if
the expectation values of a specific set of observables are known. In dimension
six, the required observables only exist if it is possible to identify six
mutually unbiased complex 6x6 Hadamard matrices. Prescribing a first Hadamard
matrix, we construct all others mutually unbiased to it, using algebraic
computations performed by a computer program. We repeat this calculation many
times, sampling all known complex Hadamard matrices, and we never find more
than two that are mutually unbiased. This result adds considerable support to
the conjecture that no seven mutually unbiased bases exist in dimension six.Comment: As published version. Added discussion of the impact of numerical
approximations and corrected the number of triples existing for non-affine
families (cf Table 3
A Factorization Algorithm for G-Algebras and Applications
It has been recently discovered by Bell, Heinle and Levandovskyy that a large
class of algebras, including the ubiquitous -algebras, are finite
factorization domains (FFD for short).
Utilizing this result, we contribute an algorithm to find all distinct
factorizations of a given element , where is
any -algebra, with minor assumptions on the underlying field.
Moreover, the property of being an FFD, in combination with the factorization
algorithm, enables us to propose an analogous description of the factorized
Gr\"obner basis algorithm for -algebras. This algorithm is useful for
various applications, e.g. in analysis of solution spaces of systems of linear
partial functional equations with polynomial coefficients, coming from
. Additionally, it is possible to include inequality constraints
for ideals in the input
The effectiveness of interventions in workplace health promotion as to maintain the working capacity of health care personal
Background: The increasing proportion of elderly people with respective care requirements and within the total population stands against aging personnel and staff reduction in the field of health care where employees are exposed to high load factors. Health promotion interventions may be a possibility to improve work situations and behavior. Methods: A systematic literature search is conducted in 32 databases limited to English and German publications since 1990. Moreover, internet-searches are performed and the reference lists of identified articles are scanned. The selection of literature was done by two reviewers independently according to inclusion and exclusion criteria. Data extraction and tables of evidence are verified by a second expert just like the assessment of risk of bias by means of the Cochrane Collaboration’s tool. Results: We identified eleven intervention studies and two systematic reviews. There were three randomized controlled trials (RCT) and one controlled trial without randomization (CCT) on the improvement of physical health, four RCT and two CCT on the improvement of psychological health and one RCT on both. Study duration ranged from four weeks to two years and the number of participants included from 20 to 345, with a median of 56. Interventions and populations were predominantly heterogeneous. In three studies intervention for the improvement of physical health resulted in less complaints and increased strength and flexibility with statistically significant differences between groups. Regarding psychological health interventions lead to significantly decreased intake of analgesics, better stress management, coping with workload, communication skills and advanced training. Discussion: Taking into consideration the small to very small sample sizes, other methodological flaws like a high potential of bias and poor quality of reporting the validity of the results has to be considered as limited. Due to the heterogeneity of health interventions, study populations with differing job specializations and different lengths of study durations and follow-up periods, the comparison of results would not make sense. Conclusions: Further research is necessary with larger sample sizes, with a sufficient study duration and follow-up, with a lower risk of bias, by considering of relevant quality criteria and with better reporting in publications
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